There are 100 people standing in line facing only one direction. They wear either a BLACK HAT or WHITE HAT but they don't know the color of the hat they are wearing. They can see all the hats directly in front of them. For example, person 97 can see and count all the hats from person 1 to 96, but has no clue on the color of his/her own hat as well as those of persons 98-100.
Now, a proctor will ask each person "what is the color of your hat?" starting from the 100th person up to the 1st (100th, 99th, 98th...1st). A person who says the wrong anwer will be eliminated.
* each person hears all the previous answers in front of him/her.
* there is no restriction on the # of black/white hats.
there can be 100W - 0B, or 50W - 50B, or 36W- 64B.
* assume that once the questioning is started, the players will always use the startegy and will never make a hum/carelessness error.
Devise a strategy that will lead to the least elimination as possible.
My guess is the person should choose the color the same as the person in front of him/her. But i don't know how to back it up with probabilities. SO please please help me..